Note that if
and
diverges, the limit comparison test gives no information. Similarly, if
and
converges, the test also provides no information. For example, consider the two series
and
These series are both
p -series with
and
respectively. Since
the series
diverges. On the other hand, since
the series
converges. However, suppose we attempted to apply the limit comparison test, using the convergent
as our comparison series. First, we see that
Similarly, we see that
Therefore, if
when
converges, we do not gain any information on the convergence or divergence of
Using the limit comparison test
For each of the following series, use the limit comparison test to determine whether the series converges or diverges. If the test does not apply, say so.
Compare this series to
Calculate
By the limit comparison test, since
diverges, then
diverges.
Compare this series to
We see that
Therefore,
Since
converges, we conclude that
converges.
Since
compare with
We see that
In order to evaluate
evaluate the limit as
of the real-valued function
These two limits are equal, and making this change allows us to use L’Hôpital’s rule. We obtain
Therefore,
and, consequently,
Since the limit is
but
diverges, the limit comparison test does not provide any information.
Compare with
instead. In this case,
Since the limit is
but
converges, the test still does not provide any information.
So now we try a series between the two we already tried. Choosing the series
we see that
As above, in order to evaluate
evaluate the limit as
of the real-valued function
Using L’Hôpital’s rule,
Since the limit is
and
converges, we can conclude that
converges.
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Leaves accumulate on the forest floor at a rate of 2 g/cm2/yr and also decompose at a rate of 90% per year. Write a differential equation governing the number of grams of leaf litter per square centimeter of forest floor, assuming at time 0 there is no leaf litter on the ground. Does this amount approach a steady value? What is that value?
You have a cup of coffee at temperature 70°C, which you let cool 10 minutes before you pour in the same amount of milk at 1°C as in the preceding problem. How does the temperature compare to the previous cup after 10 minutes?